Simplify tan(-x)cos(x)

Problem

tan(−x)*cos(x)

Solution

1. Apply the odd-even identity for the tangent function, which states that tan(−x)=−tan(x)

tan(−x)*cos(x)=−tan(x)*cos(x)

2. Substitute the quotient identity for tangent, where tan(x)=sin(x)/cos(x)

−tan(x)*cos(x)=−sin(x)/cos(x)⋅cos(x)

3. Simplify the expression by canceling the cos(x) terms in the numerator and denominator.

−sin(x)/cos(x)⋅cos(x)=−sin(x)

Final Answer

tan(−x)*cos(x)=−sin(x)

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